| Popis: |
This chapter presents the iterative residual correction (IRC) method for functional spaces, in particular, in the computational framework of functoids. The method of IRC is a well-known computational technique for improving the accuracy of an approximation to the solution of equations, especially linear equations. Until recently, this method was applied in the context of problems cast in modular number systems, such as floating-point representation systems. Functoids and their corresponding roundings have a great similarity to floating-point number structures and their roundings. The chapter reviews the IRC process in a floating-point system with particular emphasis on two arithmetic features: (1) the need for increasing accuracy in the computation of residuals during the process and (2) the propagation of information among the digits in a floating-point system that the IRC process engenders in a floating-point system. The chapter describes the latter feature in a context for achieving annihilation of digits in the residuals, and it is this feature that motivates the subsequent treatment of IRC in function spaces. |
